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Z-Squared Necklace

The signature piece for Tom Banchoff's 1996 artshow, Surfaces Beyond the Third Dimension, this image shows five views of the graph of the complex squaring function, each from a different viewpoint in complex 2-space (or real 4-space). They are part of a sequence formed by rotating the graph in four dimensions (or equivalently, walking around the graph). The rotation is chosen so that, as a projection into a plane, the image has three-fold rotational symmetry (the boundary curves form epi- and hypocycloids of a circle).

Movies and a more complete discussion of the mathematics behind this image are available at the virtual art exhibit. This surface is also the subject of Z-Squared Tetraview.

[Link] Z-Squared Necklace in SB3D

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Created: 13 Oct 2003
Last modified: Oct 15, 2003 11:26:55 AM
Comments to: dpvc@union.edu
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